We present a simple method to approximate Rao's distance between multivariate normal distributions based on discretizing curves joining normal distributions and approximating Rao's distances between successive nearby normal distributions on the curves by the square root of Jeffreys divergence, the symmetrized Kullback-Leibler divergence. We consider experimentally the linear interpolation curves in the ordinary, natural and expectation parameterizations of the normal distributions, and compare these curves with a curve derived from the Calvo and Oller's isometric embedding of the Fisher-Rao $d$-variate normal manifold into the cone of $(d+1)\times (d+1)$ symmetric positive-definite matrices [Journal of multivariate analysis 35.2 (1990): 223-242]. We report on our experiments and assess the quality of our approximation technique by comparing the numerical approximations with both lower and upper bounds. Finally, we present several information-geometric properties of the Calvo and Oller's isometric embedding.

翻译：我们提出了一种简单的方法来近似多元正态分布之间的Rao距离，该方法基于离散化连接正态分布的曲线，并通过Jeffreys散度（对称化的Kullback-Leibler散度）的平方根来近似曲线上相邻近正态分布之间的Rao距离。我们实验性地考虑了正态分布在普通参数化、自然参数化和期望参数化下的线性插值曲线，并将这些曲线与由Calvo和Oller提出的Fisher-Rao $d$ 元正态流形到$(d+1)\times (d+1)$对称正定矩阵锥的等距嵌入（源自《多元统计分析杂志》35.2 (1990): 223-242）所导出的曲线进行了比较。我们报告了实验结果，并通过将数值近似与上下界进行比较来评估我们近似技术的质量。最后，我们介绍了Calvo和Oller等距嵌入的若干信息几何性质。